Inequalities for eigenvalues of the biharmonic operator
Gerald N. Hile, R. Z. Yeh · Pacific Journal of Mathematics · 1984
Let D be a bounded domain in R m with smooth boundary.The first n + 1 eigenvalues for the problem Δ 2 w-αw = 0 in/), w = ^ = 0 on oD on satisfy the inequality For the first two eigenvalues we have the stronger bound μ 2 < 7.103 μ, (in/? 2 ), μ 2 < 4.792 μ, (in/? 3 ).The first two eigenvalues for the problem Δ 2 « + MM = 0 inZ), u = -r-= 0 on ΘZ) satisfy the inequality * 2 <2.5 », (in/? 2 ), v 2 <2.\2v x (in/? 3 ).